An adult struggles to calculate multi-player Roshambo outcomes without explicitly
enumerating clenched fists, open palms, and two fingers. Doctor Ian explains why
neither permutations nor combinations applies to such a scenario of replacement
without regard to order; Doctor Peterson introduces a new approach.

I'm looking for the derived formula solution for the following problem
someone posted in a math echo: There are seven dice. Each die has six
faces. How many different combinations are there of these seven dice?